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Probability and Statistics
This page contains resources about Probability Theory and Statistics in general. More specific information is included in each subfield. Subfields and Concepts See Category:Probability and Statistics for all its subfields. * Statistical Inference / Inferential Statistics ** Frequentist Inference *** Statistical Hypothesis Testing / Statistical Tests **** Fisher's Null Hypothesis Testing **** Neyman-Pearson Theory **** Analysis of Variance (ANOVA) **** Analysis of Covariance (ANCOVA) **** Multivariate Analysis of Variance (MANOVA) **** T-test **** F-test **** Tests of Goodness-of-Fit *** Confidence Intervals *** Bootstrapping ** Bayesian Inference *** Bayes Factor *** Credible Intervals *** Variational Bayesian Inference *** Bayesian Nonparametrics *** Empirical Bayes / Maximum Marginal Likelihood *** Hierarchical Bayes ** Inductive inference ** Causal Inference ** Interval Estimation ** Estimation Theory / Point Estimation *** Least Squares filters *** Kalman filter *** Wiener filter *** Monte Carlo Methods *** Expectation-Maximization Algorithm *** Maximum Likelihood Estimator (MLE) *** Maximum a posteriori (MAP) estimator *** Bayes Estimator **** Bayesian Decision Theory ** Decision Theory *** Neyman-Pearson Theory *** The Expected Loss Principle *** Optimal decision rules *** Bayesian Decision Theory / Bayesian Estimator *** Cost function / Loss function *** Risk function *** Admissibility *** Unbiasedness *** Minimaxity ** Algorithmic Information Theory *** Minimum Description Length (MDL) *** Minimum Message Length (MML) *** Occam's Razor *** Kolmogorov Complexity ** Model Selection and Evaluation *** Akaike Information Criterion (AIC) *** Bayesian Information Criterion (BIC) *** Deviance Information Criterion (DIC) *** Bayesian Predictive Information Criterion (BPIC) *** Focused Information Criterion (FIC) *** Bayesian Model Selection / Bayesian Model Comparison **** Bayesian Model Averaging *** Bayesian Parameter Estimation **** Bayesian Nonparametrics *** Minimum Description Length (MDL) *** Minimum Message Length (MML) *** Akaike Final Prediction Error (FPE) *** Parzen's Criterion Autoregressive Transfer Function (CAT) *** Cross-Validation *** Statistical Hypothesis Testing (for Multilevel Models / Nested Models only) **** Lagrange multiplier test / Score test / Score Method **** Likelihood-ratio test **** Wald test * Statistical Models ** Regression Analysis *** Linear Regression Model *** Simple Linear Regression *** Multiple Linear Regression (not to be confused with Multivariate Linear Regression) *** General Linear Model / Multivariate Linear Regression *** Generalized Linear Model (GLM or GLIM) *** Poisson Regression *** Least Squares Methods **** Ordinary Least Squares / Linear Least Squares **** Weighted Least Squares **** Nonlinear Least Squares *** Logistic Regression Model / Logit Model *** Probit Model *** Fixed Effects Model *** Hierarchical Linear Models / Multilevel Models / Nested Data Models **** Random Effects Model / Variance Components Model **** Mixed Effects Models (not to be confused with Mixture Models) *** Nonparametric Regression Models *** Nonlinear Regression Models *** Robust Regression Models *** Random sample consensus (RANSAC) *** Regularization **** Ridge regression / Tikhonov regularization **** Least absolute shrinkage and selection operator (LASSO) **** Elastic Nets ** Probabilistic Models *** Stochastic Models (Stochastic Processes, Random Fields, ...) *** Probabilistic Graphical Models *** Latent Variable Models (i.e. Partially Observed Probabilistic Models) **** Continuous Latent Variable Models **** Discrete Latent Variable Models ** State Space Models *** Time Series Models * Probability Theory ** Random Variables *** Continuous Random Variables **** Probability Density Function *** Discrete Random Variables **** Probability Mass Function *** Jointly Distributed Random Variables **** Joint Density Function *** Independent Random Variables *** Uncorrelated Random Variables ** Moments of a distribution *** First Moment / Mean *** Second Moment / Variance *** Third Moment / Skewness *** Fourth Moment / Kurtosis ** Probabilistic Models ** Stochastic Convergence ** Probability Space ** Measure Space ** State Space ** Theorem of Total Probability ** Central Limit Theorem ** Queueing Theory ** Martingale Theory ** Ergodic Theory ** Decision Theory ** Measure Theory ** Utility Theory Online Courses Video Lectures *Probabilistic Systems Analysis and Applied Probability by John Tsitsiklis *Introduction to Probability - The Science of Uncertainty by edX - very similar to the above *Probability by Salman Khan *Statistics by Salman Khan *Combinations - Counting Using Combinations Lecture Notes *Introduction to Probability and Statistics by Dmitry Panchenko *Economic Theory I by Eric Zivot Books Statistical Inference and Theory of Statistics * Bruce, P., & Bruce, A. (2017). Practical Statistics for Data Scientists: 50 Essential Concepts. O'Reilly Media. * Imbens, G. W., & Rubin D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. * Ross, S. M. (2014). Introduction to probability models. 11th Ed. Academic Press. * Smith, R. C. (2013). Uncertainty quantification: theory, implementation, and applications. SIAM. * Gentle, J. E. (2013). Theory of statistics. (link) * DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. 4th Ed. Pearson. * Abu-Mostafa, Y. S., Magdon-Ismail, M., & Lin, H. T. (2012). Learning From Data. AMLBook. * Diez, D. M., Barr, C. D., & Cetinkaya-Rundel, M. (2012). OpenIntro Statistics. CreateSpace. * Ramachandran, K. M., & Tsokos, C. P. (2012). Mathematical Statistics with Applications in R. Elsevier. * Gentle, J. E. (2007). Matrix algebra: theory, computations, and applications in statistics. Springer Science & Business Media. * Rice, J. (2006). Mathematical statistics and data analysis. 3rd Ed. Duxbury Press. * Cox, D. R. (2006). Principles of statistical inference. Cambridge University Press. * Lavine, M. (2005). Introduction to Statistical Thought. Michael Lavine. * Young, G. A., & Smith, R. L. (2005). Essentials of statistical inference. Cambridge University Press. * Lehmann, E. L., & Casella, G. (2003). Theory of point estimation. Springer. * Bertsekas, D. P., & Tsitsiklis, J. N. (2002). Introduction to Probability. Athena scientific. * Casella, G., & Berger, R. L. (2002). Statistical inference. Cengage Learning. * Garthwaite, P. H., Jolliffe, I. T., & Jones, B. (2002). Statistical inference. Oxford University Press. * Shao, J. (2000). Mathematical Statistics. Springer. * Mukhopadhyay, N. (2000). Probability and statistical inference. CRC Press. * Schervish, M. J. (1995). Theory of statistics. Springer Science & Business Media. Regression Analysis and Generalized Linear Models * Harrell, F. (2015). Regression modeling strategies. 2nd Ed. Springer. * Chatterjee, S., & Hadi, A. S. (2012). Regression analysis by example. 5th Ed. John Wiley & Sons. * Goldstein, H. (2010). Multilevel statistical models. 4th Ed. John Wiley & Sons. * Dobson, A. J., & Barnett, A. (2008). An introduction to generalized linear models. 3rd Ed. CRC press. * Fox, J. (2008). Applied regression analysis and generalized linear models. 2nd Ed. Sage Publications. * Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press. * Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression. Cambridge University Press. * Faraway, J. J. (2002). Practical regression and ANOVA using R. (link) * Draper, N. R., & Smith, H. (1998). Applied regression analysis. 3rd Ed. John Wiley & Sons. * Long, J. S., & Freese, J. (1997). Regression models for categorical dependent variables. Sage Publications. * McCullagh, P., & Nelder, J. A. (1989). Generalized linear models. CRC press. Counting and Probability * Shu, Z. (2016). Probability and Expectation (Volume 14). World Scientific. * Zhou, X. (2015). Counting: Math for Gifted Students. CreateSpace. * Hollos, S. & Hollos, J. R. (2013). Probability Problems and Solutions. Abrazol Publishing. * Patrick, D. (2007). Introduction to Counting and Probability. 2nd Ed. AoPS Incorporated. * Patrick, D. (2007). Intermediate Counting and Probability. AoPS Incorporated. Software See List of Statistical packages for a complete list. * The Lightspeed Matlab Toolbox * Statistics and Machine Learning Toolbox - MATLAB * Statistical functions (scipy.stats) - Python * Statistics (numpy) - Python * Statsmodels - Statistical Modeling and Econometrics in Python * revrand - Python See also * Statistical Learning Theory * Statistical Signal Processing * Information Theory * Optimization * Combinatorics * International Mathematical Olympiad Other Resources *Video Tutorials - Youtube channel of 'Mathematical Monk' *Probability and Statistics by Khan Academy *Statistics by Wikibooks *Statistics by Wikiversity *Statistics - Notebook *Probability Theory - Notebook *Algorithmic Information Theory - Notebook *Bayesian statistics: a comprehensive course by Ox Educ - Youtube *Random - Lessons in Probability, Mathematical Statistics and Stochastic Processes *Learning Machine Learning — Probability Theory Fundamentals - Medium Category:Probability and Statistics